Question 1202960: A number is chosen at random from 1 to 600 inclusive. What is the probability that it will have at least 2 digits equal to 5?
Answer by math_tutor2020(3816)   (Show Source):
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Answer: 1/25
Explanation:
Let x be a number from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
In the case of 55x, there are 10 values possible
550, 551, 552, 553, 554, 555, 556, 557, 558, 559
The same goes for the 5x5 case
505, 515, 525, 535, 545, 555, 565, 575, 585, 595
However notice how 555 has been repeated.
This means we have really introduced 9 extra cases (not 10) to have 10+9 = 19 cases so far.
Then for the x55 case we have 6 more values, but we'll exclude 555 of course.
55, 155, 255, 355, 455, 555
So we're adding 5 more cases to get 19+5 = 24 cases total
Here are all 24 items arranged in a 6 row 4 column table
| 55 | 155 | 255 | 355 | | 455 | 505 | 515 | 525 | | 535 | 545 | 550 | 551 | | 552 | 553 | 554 | 555 | | 556 | 557 | 558 | 559 | | 565 | 575 | 585 | 595 |
There are 24 values that have at least two digits of 5, out of 600 values total.
24/600 = (1*24)/(25*24) = 1/25 is the fractional probability of getting such a value.
1/25 = 0.04 in decimal form.
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